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Orbital magnetic states in moiré graphene systems

Abstract

Moiré graphene systems have attracted considerable attention in the past 3 years because they exhibit exotic phenomena including correlated insulating states, unconventional superconductivity and the quantum anomalous Hall effect. All these phenomena are intimately related to the valley-spin-degenerate and topologically non-trivial flat bands in moiré graphene systems. When time-reversal symmetry is broken spontaneously, such flavour-degenerate topological flat bands exhibit unconventional orbital magnetism associated with real-space current-loop patterns on the moiré length scale. In this Perspective, we first survey key experimental progress on the correlated insulating states and the quantum anomalous Hall phenomena. Most of these phenomena are related to the moiré orbital magnetic states, which originate from the topological nature of the moiré flat bands. Finally, we discuss theoretical progress in the understanding of the correlated insulating and quantum anomalous Hall phenomena from the perspective of spontaneous symmetry breaking.

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Fig. 1: Moiré graphene systems.
Fig. 2: Correlated insulators in twisted graphene systems.
Fig. 3: Quantum anomalous Hall effects in moiré graphene systems.
Fig. 4: Band structures and topological properties of moiré graphene systems.
Fig. 5: Moiré orbital ferromagnetism.
Fig. 6: A pseudo-Landau-level picture for twisted bilayer graphene (TBG).

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Acknowledgements

J.L. acknowledges a start-up grant from ShanghaiTech University and the National Key R&D programme of China (Grant No. 2020YFA0309601). X.D. acknowledges financial support from the Hong Kong Research Grants Council (Project No. GRF16300918 and No. 16309020).

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Glossary

Berry phases

The Berry phase of a Bloch eigenstate is a gauge-invariant phase angle accumulated after an adiabatic and cyclic evolution of the Bloch state in a vector parameter space, which can be the Brillouin zone in a crystalline solid.

Chern numbers

In topological band theory, the Chern number C of an energy band in a 2D crystalline solid is defined as the integration of the Berry curvature over the Brillouin zone.

Density matrix renormalization group

A numerical variational technique devised to solve for the Hamiltonians of low-dimensional quantum many-body systems based on efficient truncations of the many-body Hilbert space.

Filling

The filling factor p is defined as the number of electrons or holes per moiré supercell divided by the fourfold spin-valley degeneracy. p is positive/negative for electron/hole filling with respect to charge neutrality.

Hubbard model

A simple model of interacting particles in a lattice, with only two terms in the Hamiltonian: a kinetic term allowing for hopping of particles between sites of the lattice, and a potential term consisting of an on-site interaction.

Landau levels

(LL). The quantized energy levels of a 2D electron gas subject to strong perpendicular magnetic fields.

Superconducting domes

A dome-shaped superconducting region that appears in the phase diagrams of many unconventional superconductors such as cuprate superconductors and iron-based superconductors.

Superfluid weight

Non-zero superfluid weight (Ds) is a defining property of superconductors and leads to the Meissner effect and dissipationless transport. It can be more rigorously defined as the change in the free energy density \({\mathcal{F}}\) due to the motion of Cooper pairs with uniform momentum ps: \({\mathcal{F}}={D}_{{\rm{s}}}{p}_{{\rm{s}}}^{2}\,/\,8\).

Van Hove singularities

A singularity (non-smooth point) in the density of states of a crystalline solid.

Weyl nodes

In band theory, a twofold band degeneracy point at an arbitrary point in the Brillouin zone of a 3D crystalline solid.

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Liu, J., Dai, X. Orbital magnetic states in moiré graphene systems. Nat Rev Phys 3, 367–382 (2021). https://doi.org/10.1038/s42254-021-00297-3

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